The dynamics of shock wave propagation far downstream of an abrupt area expansion

Abstract

Predicting the transient flow fields that develop when a shock wave passes through an area expansion is a fundamental problem in compressible fluid mechanics and significant in many engineering applications. Experiments, large eddy simulations and geometrical shock dynamics are used to study the mechanism by which a normal shock wave that expands across an area expansion evolves into a uniform normal shock far downstream of it. This study analyses shock waves with moderate Mach numbers of 1.1–1.8 that expand at area ratios of up to 5. As the shock wave propagates into the expanded region, it experiences rapid deceleration, forming a non-uniform shock front. Impinging on the walls of the larger cross-section region, the shock wave reflects and generates a complex and highly transient shock pattern near the expansion region. We have found that as the shock front propagates further downstream, a laterally moving shock wave that intersects the shock front at a triple point reverberates laterally between the walls. This process effectively evens out the flow behind the incident shock front, thus reducing the variation of properties behind it. The extended duration of this process leads to significant pressure fluctuation behind the shock front. The results show that the evolution of the shock front can be scaled using the expanded region height and the velocity of the shock wave far downstream of the expansion. The results enabled the formulation of a simple empirical relation, allowing us to predict the shock velocity far downstream of gradual and abrupt area expansions.